## 1. GMM Regression Output for SSA Real GDP Growth

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### I. Overview and paper structure
- Three policy questions addressed:
  - What is the expected impact of the global slowdown on growth of sub-Saharan African countries?
  - What is the expected impact of changes in commodity prices and the terms of trade?
  - What is the role of global financial links in the region?
- Organization:
  - Section II: summarizes relevant findings in previous studies.
  - Section III: briefly reviews transmission channels.
  - Section IV: provides quantitative estimates of spillovers using dynamic cross-country regressions.
  - Section V: applies the growth estimates to decompose growth projections into spillovers and other effects and tests the spillover model in- and out-of-sample.
  - Section VI: concluding remarks.

### Key empirical approach
- Sample and data:
  - Sample covers 40 countries and uses annual data for 1980–2008.
- Estimation method:
  - Dynamic panel growth regression estimated with the Arellano-Bond GMM estimator.
  - Model specification: g = c + Xβ + ε for country i = 1,...,n
- Explanatory variables X include:
  - world growth weighted by partner-country trade (W),
  - oil prices,
  - non-oil prices (PNF),
  - a measure of global financial stress (STR_USA_TED),
  - country fixed effects.
- Appendix variable definitions (as used in the panel regression):
  - Y = Real GDP growth (local constant currency), in percent.
  - W = Real GDP growth of the trading partners (Local constant currency, weighted by exports), in percent.
  - X/GDP = Exports of goods and services in percent of GDP.
  - (Xoil-Moil)/GDP = Net exports of oil products in percent of GDP.
  - ToT = Growth rate of terms of trade of goods and services (price of exports divided by price of imports).
  - PNF = Annual percent change in the price of country specific non-fuel commodities (weighted average for each country).
  - POil > 5 = Threshold dummy for oil price with income effects for absolute price changes greater than 5 percent.
  - FIN = Dummy equal to 1 for financially developed and frontier markets, 0 otherwise.
  - STR_USA_TED = Spread between 3-month Libor rate and short term treasury bills rate in the United States (measure of global financial conditions).

### Main quantitative findings (estimated spillovers and price effects)
- World growth spillovers:
  - A 1 percentage point slowdown in the rest of the World leads to an estimated 0.4-0.5 percentage point slowdown in sub-Saharan African countries.
  - Effect split between contemporaneous and the following year:
    - contemporaneous effect: 0.2 percentage points
    - following-year effect: 0.2 percentage points
  - Abstracting from terms-of-trade or commodity price changes the estimated effect of world growth is 0.67, with a coefficient of about 0.5 contemporaneously.
- Non-fuel commodity prices (income effects):
  - A nonfuel-commodity-prices-induced income reduction by 10 percent tends to reduce growth in sub-Saharan Africa by about 1.9 percentage points after two years.
  - Example (Table 1 context): assuming exports of about 40 percent of GDP, a 25 percent drop in nonfuel commodity prices would lower the growth rate by about 1.9 percentage points within two years.
- Oil-price channel:
  - Oil price shocks are significant only above a threshold set at 5 percent increase in prices.
  - Impact calculated as the oil price change (above the threshold) times the share of net oil exports.
  - Example: An oil-importing SSA country importing about 20 percent of GDP, and seeing a decline in oil prices of, say, 50 percent, could expect a growth rate some 0.5 percentage points higher than otherwise.
  - Impact is linear on price changes above the threshold and on the oil intensiveness of the economy; it appears symmetric for price increases and decreases.
  - Recursive threshold testing found 5 and 10 percent thresholds maximized coefficient magnitude and significance, with 5 percent associated with more non-zeros in the sample (about 15 percent).
- Financial channel:
  - Financial conditions proxied by the spread of 3-month LIBOR vs. US Treasury bills (STR_USA_TED) are significant.
  - A 100 basis point increase in the spread reduces growth in SSA countries by an estimated 0.5 percentage points.
  - Various other measures (high-yield corporate and bank spreads, EMBI spreads, other measures) were tested, but the financial channel is significant only for STR_USA_TED.
  - The LIBOR-to-T-bill spread appears to have a larger impact in more financially advanced countries within SSA (FIN = 1), though subgroup significance levels are less clear-cut.

### Channels of transmission — trade and finance (key statistics)
- Trade channel statistics:
  - Exports from sub-Saharan Africa to the US (as a percent of GDP) doubled from 3 percent in the early 1980s to 6 percent in the 2000s.
  - Exports to the euro area remained stable at about 6 percent in the same period.
  - Advanced economies account for three-quarters of all exports from SSA.
  - Export destinations have become more diversified, with more exports going to other emerging and developing economies.
- Financial links and flows:
  - Flows of private capital to SSA reached close to 5 percent of GDP (US$50 billion) in 2007, led by strong FDI and portfolio inflows.
  - In 2007 SSA received grants of 0.8 percent of GDP, and remittances inflows of about 1.3 percent of GDP.
  - Global financial conditions deteriorated substantially, as reflected in widened 3-month LIBOR to Treasury bill rate spreads and rises in the S&P500 Volatility Index (VIX).

### Robustness, specifications, and parameter stability
- Estimation details:
  - Panel GMM based on the Arellano-Bond estimators (44 countries, 1982 - 2008).
  - Instruments in the Arellano-Bond GMM estimator used to circumvent correlation between lagged endogenous variables and the disturbance term.
- Alternative specifications examined:
  - (i) abstracting from terms of trade or commodity price changes;
  - (ii) using simple oil and non-fuel commodity export prices without interacting with level of exports;
  - (iii) using terms-of-trade measures instead of commodity prices;
  - (iv) allowing for asymmetric effects of price changes and different thresholds for the income effect.
- Non-linear specifications:
  - Non-linear specifications tested, particularly for oil variables.
  - Using simple non-fuel and oil export prices without interacting with level of exports yields weaker results; interaction with export levels (income effects) is important.
- Recursive estimates and parameter stability:
  - Recursive estimators show parameter estimates are remarkably stable over the estimation period (about 30 years).
  - Contemporaneous world growth (W) varies within a relatively narrow band of 0.2 to 0.3 across the sample period.
  - World growth lagged once also varies within a similar range.
  - Despite stability in coefficients, continuing increases in trade and financial integration imply spillovers can be expected to rise over time, especially for countries with rapid structural change in the 80s and 90s.

### Spillovers and forecasting — out-of-sample (2009)
- Method:
  - Decomposed growth projections into spillovers and other effects using coefficients from Equation 1 in Table 1 and WEO data.
- Key quantitative results:
  - Median estimates for the region: spillover effects account for about 90 percent of the projected decline in growth in 2009.
- Country groupings by extent spillovers explain projected decline:
  - Group where projected decline is mostly consistent with spillover effects (selected examples): Benin, Burkina Faso, Cameroon, Comoros, Côte d’Ivoire, Kenya, Mali, Nigeria, Senegal.
  - Group where spillovers explain only a small fraction of projected weakening (selected examples): Angola, Botswana, Equatorial Guinea, Seychelles — domestic factors appear to worsen the situation.
  - Other countries: variation broadly explained by spillovers but with offsetting domestic factors (positive or negative).
- Selected country-level numbers (Table 2 examples):
  - Angola: Actual 2008 = 14.8; WEO/REO 2009 = -3.6; WEO/REO Δ 09/08 = -18.4; Spillover Effects = -5.6
  - Benin: Actual 2008 = 5.0; WEO/REO 2009 = 3.8; WEO/REO Δ 09/08 = -1.1; Spillover Effects = -1.2
  - Nigeria: Actual 2008 = 5.3; WEO/REO 2009 = 2.9; WEO/REO Δ 09/08 = -2.4; Spillover Effects = -2.3
  - SSA Median: Actual 2008 = 5.0; WEO/REO 2009 = 2.9; WEO/REO Δ 09/08 = -2.0; Spillover Effects = -1.8

### Spillovers and forecasting — in-sample (2008)
- WEO Spring 2008 global assumptions to forecast 2008 growth:
  - Allowing for a forecast deviation of 0.5 percentage point either way, 58 percent of the WEO forecasts were above the actual growth rate.
  - Projections were relatively optimistic for rates below 8 percent and generally pessimistic for higher rates.
  - Only 20 percent of countries were more than 0.5 percentage points below the actual rate.
- For the spillover model:
  - 37 percent of forecasts were above the actual growth rate.
  - Forecasts were optimistic at low rates and pessimistic at high rates, with low/high thresholds around 4 percent.
  - Distribution of errors for the spillover model is wider than for the WEO forecasts, likely because the spillover model does not account for domestic factors, policy responses, or idiosyncratic shocks beyond spillovers.

### Conclusions and implications
- The model shows SSA countries are significantly affected by:
  - lower external demand for exports (world growth effects),
  - declines in commodity prices and terms of trade,
  - tighter global financial conditions (proxied by STR_USA_TED).
- Four standout quantitative results:
  - (i) A slowdown in the rest of the World drives a slowdown in SSA, with contemporaneous effects; quantified as 0.4 percentage point SSA slowdown per 1 percentage point global slowdown.
  - (ii) Non-fuel commodity-price-induced income reductions have quantifiable impacts on growth; interaction with export levels matters.
  - (iii) Oil price shocks are significant with non-linear effects and no asymmetric effects found.
  - (iv) The LIBOR-to-T-bill spread is a significant proxy for global financial conditions affecting SSA growth.
- Caveats and limitations:
  - Cross-country regressions explain only part of the growth variation; factors such as the level of reserves, policy responses, and expected persistence may interact with shocks.
  - Estimates reflect short-term effects and do not embed variables in a more complete structural growth model.
  - The role of policy (fiscal, monetary, exchange rate regime, reserves) in mitigating shocks is not explored and warrants further research.

*IMF Working Paper: 1. GMM Regression Output for SSA Real GDP Growth (from _wp09155 PDF).*

### 1. GMM Regression Output for SSA Real GDP Growth ..........................................................9

### 1. GMM Regression Output for SSA Real GDP Growth ..........................................................9

### I. WORLD GROWTH SPILLOVERS — overview and paper structure
- The paper addresses three questions: What is the expected impact of the global slowdown on growth of sub-Saharan African countries? What is the expected impact of changes in commodity prices and the terms of trade? What is the role of global financial links in the region?
- Organization:
  - Section II: summarizes relevant findings in previous studies.
  - Section III: briefly reviews transmission channels.
  - Section IV: provides quantitative estimates of spillovers using dynamic cross-country regressions.
  - Section V: applies the growth estimates to decompose growth projections into spillovers and other effects and tests the spillover model in- and out-of-sample.
  - Section VI: concluding remarks.

### Key empirical approach
- Sample and data:
  - Sample covers 40 countries and uses annual data for 1980–2008.
- Empirical framework:
  - Dynamic panel growth regression estimated with the Arellano-Bond GMM estimator.
  - Model specification (as presented):
    - g = c + Xβ + ε  for country i = 1,...,n
  - Explanatory variables X include: world growth weighted by partner-country trade, oil prices, non-oil prices, a measure of global financial stress, and country fixed effects.

### Main quantitative findings (estimated spillovers and price effects)
- World growth spillovers:
  - A 1 percentage point slowdown in the rest of the World leads to an estimated 0.4-0.5 percentage point slowdown in sub-Saharan African countries.
  - The effect is split between contemporaneous (0.2 percentage points) and the following year (0.2 percentage points).
- Non-fuel commodity prices (income effects):
  - A nonfuel-commodity-prices-induced income reduction by 10 percent tends to reduce growth in sub-Saharan Africa by about 1.9 percentage points after two years (example re-expressed in Table 1 context: assuming exports of about 40 percent of GDP, a 25 percent drop in nonfuel commodity prices would lower the growth rate by about 1.9 percentage points within two years).
- Oil-price channel:
  - Oil price shocks are significant only above a threshold set at 5 percent increase in prices.
  - Impact is calculated as the oil price change (above the threshold) times the share of net oil exports.
  - Example: An oil-importing SSA country importing about 20 percent of GDP, and seeing a decline in oil prices of, say, 50 percent, could expect a growth rate some 0.5 percentage points higher than otherwise.
  - The impact is linear on price changes above the threshold and on the oil intensiveness of the economy; it appears symmetric for price increases and decreases.
- Financial channel:
  - Financial conditions proxied by the spread of 3-month LIBOR vs. US Treasury bills are significant.
  - A 100 basis point increase in the spread reduces growth in SSA countries by an estimated 0.5 percentage points.
- Average-nature and horizon:
  - Estimates reflect average effects for the average country and shock and are interpreted as short-term effects of changes in the external environment on SSA growth.

### Channels of transmission — trade and finance (key statistics)
- Trade channel:
  - Exports from sub-Saharan Africa to the US (as a percent of GDP) doubled from 3 percent in the early 1980s to 6 percent in the 2000s.
  - Exports to the euro area remained stable at about 6 percent in the same period.
  - Advanced economies account for three-quarters of all exports from SSA.
  - Export destinations have become more diversified, with more exports going to other emerging and developing economies.
- Financial links and flows:
  - Flows of private capital to SSA reached close to 5 percent of GDP (US$50 billion) in 2007, led by strong FDI and portfolio inflows (flows concentrated in a few countries and mainly targeted at extractive industries).
  - In 2007 SSA received grants of 0.8 percent of GDP, and remittances inflows of about 1.3 percent of GDP.
  - Global financial conditions deteriorated substantially, as reflected in widened 3-month LIBOR to Treasury bill rate spreads and rises in the S&P500 Volatility Index (VIX).

### Robustness, comparisons, and caveats
- Comparison with previous studies:
  - Ndulu and O’Connell (2007) found a 1 percent rise in trading partner growth raises country growth by 0.4 percent (half-decadal average, global regression setting).
  - Deaton (1996) found a decline in non-fuel commodity prices of 10 percent could reduce SSA GDP by about 1.5 percent (cumulative effect on thrice-lagged growth of commodity prices).
  - Collier and Goderis (2007) find positive short-term output effects of terms of trade shocks but adverse longer-term effects in countries with weak institutions.
- Two caveats highlighted by the authors:
  1. The cross-country regressions explain only part of the growth variation experienced by SSA countries; factors such as the level of reserves, policy responses, and expected persistence may interact with shocks.
  2. The estimates reflect short-term effects and do not embed variables in a more complete structural growth model.

*IMF Working Paper: 1. GMM Regression Output for SSA Real GDP Growth (from _wp09155 PDF).*

### 0.5 percentage point higher within two years.

### _wp09155 - 0.5 percentage point higher within two years.

### Key empirical findings
- On average, over the last almost 30 years, a 1 percentage point slowdown in the rest of the World has led to an estimated 0.4 percentage point slowdown in SSA countries.  
- Abstracting from terms-of-trade or commodity price changes the estimated effect of world growth is 0.67, with a coefficient of about 0.5 contemporaneously.  
- The financial channel, proxied by the spread of 3-month LIBOR vs. US Treasury bills (STR_USA_TED), is significant: a 100 basis point increase in the spread reduces growth in SSA countries by an estimated 0.5 percentage point.  
- Oil price shocks are significant, with no evidence of asymmetric effects; non-linear effects are present and thresholds of 5 and 10 percent offered maximum coefficient value and significance for income-related oil shocks.  
- Using simple non-fuel and oil export prices without interacting with level of exports yields weaker results; interaction with export levels (income effects) is important.

### Robustness, specifications, and estimation
- Estimation method: Panel GMM based on the Arellano-Bond estimators (44 countries, 1982 - 2008).  
- Instruments in the Arellano-Bond GMM estimator are used to circumvent correlation between lagged endogenous variables and the disturbance term.  
- Alternative specifications examined in Table 1:
  - (i) abstracting from terms of trade or commodity price changes;
  - (ii) using simple oil and non-fuel commodity export prices without interacting with level of exports;
  - (iii) using terms-of-trade measures instead of commodity prices;
  - (iv) allowing for asymmetric effects of price changes and different thresholds for the income effect.
- Non-linear specifications tested, particularly for oil variables; recursive threshold testing found 5 and 10 percent thresholds maximized coefficient magnitude and significance, with 5 percent associated with more non-zeros in the sample (about 15 percent).

### Recursive estimates and parameter stability
- Recursive estimators of the GMM model show parameter estimates are remarkably stable over the estimation period (about 30 years).  
- Contemporaneous world growth (W) varies within a relatively narrow band of 0.2 to 0.3 across the sample period.  
- World growth lagged once also varies within a similar range.  
- Despite stability in estimated coefficients, continuing increases in trade and financial integration imply spillovers can be expected to rise over time, especially for countries with rapid structural change in the 80s and 90s.

### Financial channel details
- Various measures of global financial stress were tested (high-yield corporate and bank spreads, EMBI spreads, other measures), but the financial channel is significant only for the initial measure: the short term U.S. dollar-Libor spread (STR_USA_TED).  
- The LIBOR-to-T-bill spread appears to have a larger impact in more financially advanced countries within SSA (FIN = 1), though reported significance levels are less clear-cut in subgroup analysis (results not reported).

### Spillovers and forecasting — out-of-sample (2009)
- Application: decomposed growth projections into spillovers and other effects using coefficients from Equation 1 in Table 1 and WEO data.  
- Median estimates for the region: spillover effects account for about 90 percent of the projected decline in growth in 2009.  
- Three country groups identified:
  - Group where projected decline is mostly consistent with spillover effects (examples): Benin, Burkina Faso, Cameroon, Comoros, Côte d’Ivoire, Kenya, Mali, Nigeria, Senegal.
  - Group where spillovers explain only a small fraction of projected weakening (examples): Angola, Botswana, Equatorial Guinea, Seychelles — domestic factors appear to worsen the situation.
  - Other countries: variation broadly explained by spillovers but with offsetting domestic factors (positive or negative).
- Table 2 highlights country-level numbers (selected examples):
  - Angola: Actual 2008 = 14.8; WEO/REO 2009 = -3.6; WEO/REO Δ 09/08 = -18.4; Spillover Effects = -5.6
  - Benin: Actual 2008 = 5.0; WEO/REO 2009 = 3.8; WEO/REO Δ 09/08 = -1.1; Spillover Effects = -1.2
  - Nigeria: Actual 2008 = 5.3; WEO/REO 2009 = 2.9; WEO/REO Δ 09/08 = -2.4; Spillover Effects = -2.3
  - SSA Median: Actual 2008 = 5.0; WEO/REO 2009 = 2.9; WEO/REO Δ 09/08 = -2.0; Spillover Effects = -1.8

### Spillovers and forecasting — in-sample (2008)
- Using WEO Spring 2008 global assumptions to forecast 2008 growth:
  - Allowing for a forecast deviation of 0.5 percentage point either way, 58 percent of the WEO forecasts were above the actual growth rate. Projections were relatively optimistic for rates below 8 percent and generally pessimistic for higher rates. Only 20 percent of countries were more than 0.5 percentage points below the actual rate.
  - For the spillover model, 37 percent of forecasts were above the actual growth rate. Forecasts were optimistic at low rates and pessimistic at high rates, with low/high thresholds around 4 percent.
  - The distribution of errors for the spillover model is wider than for the WEO forecasts, likely because the spillover model does not account for domestic factors, policy responses, or idiosyncratic shocks beyond spillovers.

### Conclusions and implications
- The model shows SSA countries are significantly affected by:
  - lower external demand for exports (world growth effects),
  - declines in commodity prices and terms of trade,
  - tighter global financial conditions (proxied by STR_USA_TED).
- Four standout results:
  - (i) A slowdown in the rest of the World drives a slowdown in SSA, with contemporaneous effects; quantified as 0.4 percentage point SSA slowdown per 1 percentage point global slowdown.
  - (ii) Non-fuel commodity-price-induced income reductions have quantifiable impacts on growth; interaction with export levels matters.
  - (iii) Oil price shocks are significant with non-linear effects and no asymmetric effects found.
  - (iv) The LIBOR-to-T-bill spread is a significant proxy for global financial conditions affecting SSA growth.
- Caveats:
  - Cross-country regressions explain only part of growth variation; domestic factors and policies matter.
  - Estimates reflect short-term effects; long-run impacts (e.g., from commodity price changes) are not addressed here.
  - The role of policy (fiscal, monetary, exchange rate regime, reserves) in mitigating shocks is not explored and warrants further research.

### Appendix — variables used in the panel regression (as defined)
- Y = Real GDP growth (local constant currency), in percent.  
- W = Real GDP growth of the trading partners (Local constant currency, weighted by exports), in percent.  
- X/GDP = Exports of goods and services in percent of GDP.  
- (Xoil-Moil)/GDP = Net exports of oil products in percent of GDP.  
- ToT = Growth rate of terms of trade of goods and services (price of exports divided by price of imports).  
- PNF = Annual percent change in the price of country specific non-fuel commodities (weighted average for each country).  
- POil > 5 = Threshold dummy for oil price with income effects for absolute price changes greater than 5 percent.  
- FIN = Dummy equal to 1 for financially developed and frontier markets, 0 otherwise.  
- STR_USA_TED = Spread between 3-month Libor rate and short term treasury bills rate in the United States (measure of global financial conditions).

*Source: Authors' calculations, based on the IMF working paper content provided in the PDF unit.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09155.pdf_